The Dirichlet Problem of the Constant Mean Curvature in Equation in Lorentz-Minkowski Space and in Euclidean Space
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AuthorLópez Camino, Rafael
Euclidean spaceLorentz-Minkowski spaceDirichlet problemMean curvatureMaximum principle
López, R. (2019). The Dirichlet Problem of the Constant Mean Curvature in Equation in Lorentz-Minkowski Space and in Euclidean Space. Mathematics, 7(12), 1211.
SponsorshipThis research was partially supported by grant No. MTM2017-89677-P,MINECO/AEI/FEDER, UE
We investigate the differences and similarities of the Dirichlet problem of the mean curvature equation in the Euclidean space and in the Lorentz-Minkowski space. Although the solvability of the Dirichlet problem follows standards techniques of elliptic equations, we focus in showing how the spacelike condition in the Lorentz-Minkowski space allows dropping the hypothesis on the mean convexity, which is required in the Euclidean case.